On Banach Fixed Point Theorem

Abstract

In this work, we study the Banach Fixed Point Theorem with a view to having an insight into the implication of varied contraction constants for a family of contraction maps. We prove the existence of fixed points of a family of contraction operators defined on a complete metric space. We also prove that the sequence of fixed points of a family of contraction operators defined on a complete metric characterised by a family of contraction constants converges. Finally, using examples we demonstrate that the fixed point (which it converges to) is well behaved and represent the fixed points of a family of contraction operators for given initial value.